Adjoint based shape perturbations for incremental changes in the longitudinal stability derivative using the meshfree LSKUM

Abstract

This paper presents the development of tangent linear and adjoint-over-tangent meshfree solvers to accurately compute the longitudinal static stability derivative and its shape sensitivities. These solvers are constructed using algorithmic differentiation techniques. The meshfree solver is based on the Least Squares Kinetic Upwind Method (LSKUM) for two-dimensional inviscid compressible flows. To obtain smooth shapes that make incremental changes in the stability derivative using gradient algorithms, shape sensitivities are smoothed using a two-step procedure. In the first step, sensitivities are smoothed using the Sobolev gradient smoothing. Later, the sensitivities are further smoothed using the Savitzky–Golay filter to get shapes with smooth curvature variation. The LSKUM primal, tangent, and adjoint-over-tangent solvers are applied to the test case of a subsonic flow over the MS0313 airfoil. Numerical results have shown that the adjoint-over-tangent solver computes the shape sensitivities very accurately and matches up to machine precision with the values obtained from the tangent-over-tangent solver. Perturbed airfoil shapes that increase or decrease the stability derivative are presented.